Can't thicken parts, slicers don't recognize said parts
What you are asking for is professional help to make the model printable. The problem with your model is that your 3D Printer (No matter which kind you have) is not able to print that thin clothing. Actually thats not even the real problem. The real problem is that Slic3r or Cura can not know what shape that is because is has no inside. It is just flat. Thats why it doesn't appears when sliced. I dont know if you had a look at some other dressed character figurines, but they have usually quite thick clothing. For example habe a look at models of ballerinas on thingiverse. Thats why you tried Solidify right? But wait there is more! Not only has your object to be manifold (closed) it also needs to be one non-intersecting object to be sliced correctly. Usually when the Remesh Modifier works fine on your mesh its printable. It didn't for you right? Thats because you had intersecting geometry. As I am here writing, I am not writing this to make you go: "Oh thats impossible to do for me", so I have a quick solution for you which might actually work. If it isn't perfect enough, just make it perfekt in sculpt mode. So here is what you need to do:


Make a Proxymesh of your Character in his/her posed position. What that means is: Make a mesh that surrounds your character and is really simple when it comes to the polygons. Around 200 or 300 Faces will work well I think. You should use the Mirror Modifier to make the symmetry perfect if you can (I dont know your Pose)
Add a Subdivision Surface Modifier, a Shrinkwrap Modifier and a Remesh Modifier
Tweak the Settings. Most Important is the Shrinkwrap Modifier. You have to set the mode to either Nearest Surface Point or to Project. In Case you set it to Project, which I think will work much better on your model, you have to make sure negative and maybe positive is checked and none of the X,Y,Z checkboxes are checked. The Modifier will then move the vertices of your mesh along their Normals until they hit the Surface of your model (obviously you have to specify which model in the box Target)
Apply everything, go into Sculpt Mode (use symmetry if you can) and fix everything thats not quite there
Print it!